What Is Equivalent to 5/7 Fraction?

Fractions are an essential part of mathematics and are used to represent portions of a whole. Learning equivalent fractions helps students solve mathematical problems more easily and improves their understanding of numbers. In this article, we will understand what fractions are equivalent to 5/7, how to calculate them, and their practical uses.

Understanding the Fraction 5/7

The fraction 5/7 represents five parts out of seven equal parts of a whole.

Breaking Down 5/7

• 5 (Numerator): Represents the number of selected or used parts.
• 7 (Denominator): Represents the total number of equal parts.

For example, if a pie is divided into 7 equal slices and you eat 5 slices, you have eaten 5/7 of the pie.

What Are Equivalent Fractions?

Equivalent fractions are fractions that have different numbers but represent the same value. These fractions are formed by multiplying or dividing both the numerator and denominator by the same number.

Definition

Equivalent fractions represent the same portion or value even though the numerator and denominator are different.

Some fractions equivalent to 5/7 include:

• 10/14
• 15/21
• 20/28

All of these fractions represent the same value as 5/7.

Equivalent Fractions of 5/7

To find fractions equivalent to 5/7, multiply both the numerator and denominator by the same number.

Examples of Equivalent Fractions

Multiply By	Equivalent Fraction
2	10/14
3	15/21
4	20/28
5	25/35
6	30/42
7	35/49
8	40/56
9	45/63
10	50/70

All these fractions are equal to 5/7.

How to Find Equivalent Fractions of 5/7

Equivalent fractions can be found using a simple mathematical method.

Step-by-Step Method

Step 1: Start With the Original Fraction

Example: 5/7

Step 2: Select Any Whole Number

Choose a number such as 2, 3, 4, or more.

Step 3: Multiply Both Numerator and Denominator

Example:

Multiply by 2
5 × 2 = 10
7 × 2 = 14
Equivalent fraction = 10/14

Multiply by 4
5 × 4 = 20
7 × 4 = 28
Equivalent fraction = 20/28

This method can be repeated infinitely to create multiple equivalent fractions.

Why Are Equivalent Fractions Important?

Equivalent fractions are useful for solving various mathematical problems and practical calculations.

Simplifying Fractions

Equivalent fractions help reduce fractions into simpler forms.

Example:
20/28 can be simplified to 5/7 by dividing numerator and denominator by 4.

Comparing Fractions

Equivalent fractions make it easier to compare fractions with different denominators.

Example:
5/7 and 20/28
Since both represent the same value, they are equal.

Performing Fraction Operations

Equivalent fractions help in solving addition and subtraction problems involving fractions.

Example:
5/7 + 3/14

Convert 5/7 into 10/14
Now add:
10/14 + 3/14 = 13/14

Visual Representation of Equivalent Fractions of 5/7

Equivalent fractions can be understood through visual examples.

Imagine a chocolate bar divided into equal sections:

• Dividing into 7 parts and eating 5 parts equals 5/7.
• Dividing into 14 parts and eating 10 parts still equals 5/7.
• Dividing into 21 parts and eating 15 parts also equals 5/7.

Even though the number of pieces changes, the consumed portion remains the same.

Converting 5/7 into Decimal and Percentage

Fractions can also be converted into decimal and percentage formats.

Decimal Form

To convert 5/7 into decimal:

5 ÷ 7 = 0.714285… (Repeating)

Percentage Form

To convert into percentage:

0.714285 × 100 = 71.43% (Approximately)

All equivalent fractions of 5/7 represent about 71.43% of a whole.

How to Check If Two Fractions Are Equivalent to 5/7

Cross multiplication is commonly used to verify equivalent fractions.

Example: Is 15/21 Equivalent to 5/7?

Step 1: Cross multiply
5 × 21 = 105
7 × 15 = 105

Step 2: Compare results
Since both values are equal, 15/21 is equivalent to 5/7.

Common Mistakes While Finding Equivalent Fractions

Multiplying Only Numerator or Denominator

Both numerator and denominator must be multiplied by the same number to maintain equality.

Using Different Multipliers

Using different numbers for numerator and denominator changes the value of the fraction.

Real-Life Examples of 5/7 Equivalent Fractions

Equivalent fractions are frequently used in daily activities.

Cooking Measurements

If a recipe requires 5/7 cup of water, it can also be measured as:

• 10/14 cup
• 15/21 cup
• 20/28 cup

Time Calculation

5/7 of one week equals:

7 days × 5/7 = 5 days

Academic Performance

If a student completes 5/7 of total assignments, it represents approximately 71.43% completion.

Infinite Equivalent Fractions of 5/7

There are unlimited equivalent fractions of 5/7. Some examples include:

• 55/77
• 60/84
• 75/105
• 500/700

All these fractions represent the same value as 5/7.